Sliding mode adaptive Controller for PZT actuators

In this paper a method for motion controller parameters adaptation in the framework of sliding mode control (SMC) system is presented. Design is based on minimization of a cost function selected to depend on the distance from sliding mode manifold thus providing that adaptive controller enforces sliding mode motion in a closed loop system. It has been proven that selected cost function guaranties that the global minima is reached and then the sliding mode conditions are satisfied, thus closed loop motion is robust against parameter changes and the disturbances. The design for both MIMO and SISO systems is discussed. For the controller design the system states and the nominal value of the control input matrix are used. The stability proofs are given and the controller performance is verified by experimental results. The proposed algorithm is applied to control of the PZT actuator having hysteresis nonlinearity. Experimental verification shows that very high accuracy is reached (sub-nanometer motion) while the complexity of the controller did not exceed the usual SMC control schemes.